Question

The midpoint of AB is M(3, -1). If the coordinates of A are (5,1), what are the

Answer 1

Given parameters:

Midpoint of AB =  M(3, -1)

Coordinates of A = (5,1)

Unknown:

Coordinates of B = ?

Solution:

To find the mid point of any line, we use the expression below;

              $x_{m} = \frac{x_{1} + x_{2} }{2}$    and $y_{m} = \frac{y_{1} + y_{2} }{2}$

where $x_{m}$  and $y_{m}$ = coordinates of the mid points = 3 and -1

   x₁  = 5 and y₁ = 1

  x₂ = ?  and y₂ = ?

Now let us input the variables and solve,

            3  = $\frac{5 + x_{2} }{2}$           and     -1 = $\frac{1 + y_{2} }{2}$

    5 +  x₂  = 6                          -2 = 1  + y₂

            x₂ = 1                             y₂ = -2 -1 = -3

The coordinates of B = 1, -3